介质目标电磁散射的高效积分方程方法研究

【作者】 康丽；

【导师】 胡俊；

【作者基本信息】 电子科技大学 ， 电磁场与微波技术， 2009， 硕士

【摘要】 由于在通信、雷达等领域的重要应用价值,介质目标电磁散射特性备受关注。积分方程方法由于其求解严格、计算结果精度高,成为了分析介质目标电磁散射特性的主要方法。本文主要围绕介质目标电磁散射特性的高效积分方程开展研究工作。针对传统方法求解介质目标所需未知量数目太多,矩阵方程迭代求解收敛很慢的问题,着重研究了单积分方程(SIE)和基于体无散基函数的体积分方程,并采用矩阵交叉近似技术(ACA)和多层快速多极子方法(MLFMA),进一步减少了存储量,提高了单积分方程和体积分方程的计算效率。首先,本文详细介绍了求解介质结构的面积分方程方法及目标模型的建立。研究了面积分方程方法:PMCHW,TENENH,JMCFIE。给出了公式推导,开发了PMCHW,TENENH,JMCFIE三种面积分方程的数值程序,为后面的工作打下了基础。然后,为了减少待求未知量的个数,提高矩阵求解迭代收敛速度,本文详细研究了一种高效的面积分方程方法——单积分方程方法,给出了详细的公式推导,阐述了其物理意义。并将该方法的思想分别应用于PMCHW,TENENH,JMCFIE中,推导出相应的单积分方程形式。数值研究表明,采用单积分方程方法求解介质目标电磁散射,数值结果准确,并能提高矩阵迭代收敛求解速度。接着研究了电大尺寸介质目标电磁散射分析的高效方法。由于矩量法的内存需求和计算复杂度都是O ( N 2)( N为待求未知量数目),当处理电大尺寸的介质时,采用矩量法求解需要昂贵的内存开销和CPU计算时间。本文采用高效方法——ACA算法,成功地解决了单积分方程矩量法求解所带来的内存消耗大和计算复杂度高的问题。最后,本文分析了用于体积分方程的体无散基函数,详细推导了基于此基函数矩量法的具体公式,重点介绍了求解过程中的奇异性处理技术,成功实现了基于体无散基函数的多层快速多极子方法,为三维非均匀介质电磁散射提供了高效的数值分析工具。更多还原

【Abstract】 The electromagnetic scattering of dielectric bodies has been extensively studied because of its importance in the area of wireless communication and radar. The integral equation is widely applied to analyze the electromagnetic scattering of dielectric objects for its high precision. In this thesis, the research work is based on efficient integral equations for electromagnetic scattering property of dielectric materials. Single integral equation(SIE) and volume integral equation with the solenoidal basis function are investigated. The number of the unknowns is reduced and the iterative solution of the matrix equation is more efficient than the traditional methods. Two efficient methods including adaptive cross approximation (ACA) algorithm and multilevel fast multipole algorithm (MLFMA) are adopted to reduced the storage requirement and computational cost successfully.Firstly, the surface integral equation method for dielectric objects is introduced. Surface integral equations for dielectric objects based on equivalent principle, such as PMCHW, TENENH, JMCFIE are presented in detail. Numerical results show that the programs are correct.Secondly, a novel surface integral equation called single integral equation is presented to realize efficient solution of scattering from dielectric objects. Further, the SIE is extended successfully into the PMCHW,TENENH and JMCFIE. Numerical results by this method are in good agreement with the exact results. And, the convergence speed of the iterative solution of the matrix equation in SIE method is significantly better than that of the traditional coupled integral equations method. Then, the efficient integral method for electromagnetic scattering property of electrically-large object is investigated. Since the memory requirement and computational complexity are both O ( N 2), where N is the number of unknowns. It requires very expensive storage and CPU time when dealing with the electrically-large object. In this thesis, a efficient method called ACA algorithm is adopted to further reduce the storage requirement and computational complexity successfully.Finally, the solenoidal basis function for the volume integral equation is studied. The detailed formulations for implementation, especially the technique for treating singular integration in the method of moment are given. Numerical results show that the proposed approach is valid. The MLFMA algorithm is successfully realized for the volume integral equation solution. It provides an efficient analysis tool for numerical solution of scattering from 3D inhomogeneous dielectric.更多还原